Discrimination Analysis Used with Optical Computing Devices

ABSTRACT

Disclosed are systems and methods that use discriminant analysis techniques and processing in order to reduce the time required to determine chemical and/or physical properties of a substance. One method includes optically interacting a plurality of optical elements with one or more known substances, each optical element being configured to detect a particular characteristic of the one or more known substances, generating an optical response from each optical element corresponding to each known substance, wherein each known substance corresponds to a known spectrum stored in an optical database, and training a neural network to provide a discriminant analysis classification model for an unknown substance, the neural network using each optical response as inputs and one or more fluid types as outputs, and the outputs corresponding to the one or more known substances.

BACKGROUND

The present invention relates to optical computing devices and, moreparticularly, to using discriminant analysis techniques and processingwith optical computing devices in order to reduce the time required fordetermination of chemical and/or physical properties of a substance.

In the oil and gas industry, it can be important to determine preciselythe characteristics and chemical compositions of fluids circulating intoand out of subterranean hydrocarbon-bearing formations. Typically, theanalysis of fluids related to the oil and gas industry is conductedoff-line using laboratory analyses, such as spectroscopic and/or wetchemical methods, which analyze an extracted sample of the fluid.Depending on the analysis required, however, such an approach can takehours to days to complete, and even in the best-case scenarios, a jobwill often be completed prior to completion of the analysis.

Off-line, retrospective analyses can further be unsatisfactory foraccurate determination of fluid characteristics, because thecharacteristics of an extracted sample of the fluid often change duringthe lag time between collection and analysis, thereby rendering themeasured properties of the sample non-indicative of the true chemicalcomposition or characteristic. Factors that can alter thecharacteristics of a fluid during the lag time between collection andanalysis can include, for example, scaling, reaction of variouscomponents in the fluid with one another, reaction of various componentsin the fluid with components of the surrounding environment, simplechemical degradation, and bacterial growth.

Furthermore, accurate off-line laboratory analyses of a fluid sample cansometimes be difficult to perform because of unknown contaminants. Forexample, the collection of the sample in the field is typically obtainedusing a probe-type tool. However, it is difficult to know with certaintythat the sample obtained is virgin formation fluid, rather thanformation fluid contaminated with drilling fluid. While analyses of afluid sample consisting solely of formation fluid may be accurate, acontaminated fluid sample is more likely to render inaccurate data.Although off-line retrospective analyses of a fluid can be satisfactoryin certain cases, there are several drawbacks to such methods where areal-time or near real-time analysis would otherwise be a more effectivemethod.

BRIEF DESCRIPTION OF THE DRAWINGS

The following figures are included to illustrate certain aspects of thepresent invention, and should not be viewed as exclusive embodiments.The subject matter disclosed is capable of considerable modifications,alterations, combinations, and equivalents in form and function, as willoccur to those skilled in the art and having the benefit of thisdisclosure.

FIG. 1 illustrates an exemplary integrated computation element,according to one or more embodiments.

FIG. 2 illustrates exemplary transmittance spectra corresponding to aplurality of ICE components that are spanned over the optical wavelengthof interest for a known substance.

FIG. 3 illustrates optical responses of the plurality of ICE componentsused to create the transmittance spectra of FIG. 2.

FIG. 4 illustrates an exemplary neural network structure for classifyinga sample substance using qualitative discriminant analysis.

FIGS. 5 a-5 e depict exemplary classification outputs derived whiletraining the neural network structure of FIG. 4.

FIG. 6 illustrates the optical or spectral responses of ten ICEcomponents in view of three unknown fluid samples.

FIG. 7 illustrates fluid type index outputs for each of the threeunknown fluid samples of FIG. 6 as corresponding to their respectiveoptical responses.

FIG. 8 illustrates an exemplary neural network structure for quantifyinga sample substance using quantitative discriminant analysis.

FIGS. 9 a-9 f provide six comparison plots for six calibration models,respectively, according to one or more embodiments.

FIG. 10 illustrates a cross plot that provides quantitative measurementdata derived from the trained neural network of FIG. 8 upon testingthree unknown samples, according to one or more embodiments.

FIG. 11 illustrates another cross plot that provides quantitativemeasurement data derived from the trained neural network of FIG. 8 upontesting three unknown samples, according to one or more embodiments.

DETAILED DESCRIPTION

The present invention relates to optical computing devices and, moreparticularly, to using discriminant analysis techniques and processingwith optical computing devices in order to reduce the time required fordetermination of chemical and/or physical properties of a substance.

The present disclosure discusses the use of optical computing devices,also referred to as “opticoanalytical devices,” for the real-time ornear real-time monitoring of a substance, or a sample of a substance.Exemplary optical computing devices receive an input of electromagneticradiation associated with a substance and produce an output ofelectromagnetic radiation from an optical element arranged within theoptical computing device. The optical element may be, for example, anintegrated computational element (ICE), also known as a multivariateoptical element (MOE). The electromagnetic radiation that opticallyinteracts with the processing element is changed so as to be readable bya detector, such that an output of the detector can be correlated to aparticular characteristic of the substance.

Such optical computing devices can advantageously provide real-time ornear real-time monitoring that cannot presently be achieved with eitheronsite analyses at a job site or via more detailed analyses that takeplace in a laboratory. A significant and distinct advantage of thesedevices is that they can be configured to specifically detect and/ormeasure a characteristic of interest of a substance, such as chemicaland/or physical properties of the substance, thereby allowingqualitative and/or quantitative analyses of the substance to occurwithout having to extract a sample and undertake time-consuming analysesof the sample at an off-site laboratory.

As used herein, the term “characteristic” refers to a chemical,mechanical, or physical property of a substance, such as a quantitativeor qualitative value of one or more chemical constituents or compoundspresent therein or any physical property associated therewith.Illustrative characteristics that can be monitored with such opticalcomputing devices can include, for example, chemical composition (e.g.,identity and concentration in total or of individual components), phasepresence (e.g., gas, oil, water, etc.), impurity content, pH,alkalinity, viscosity, density, ionic strength, total dissolved solids,salt content (e.g., salinity), porosity, opacity, bacteria content,total hardness, combinations thereof, state of matter (solid, liquid,gas, emulsion, mixtures, etc), and the like.

As used herein, the term “optical computing device” refers to an opticaldevice that is configured to receive an input of electromagneticradiation associated with a substance, such as a fluid and produce anoutput of electromagnetic radiation from a processing element arrangedwithin the optical computing device. The processing element may be, forexample, an integrated computational element (ICE) used in the opticalcomputing device. The electromagnetic radiation that optically interactswith the processing element is changed so as to be readable by adetector, such that an output of the detector can be correlated to acharacteristic of the fluid or a phase of the fluid. The output ofelectromagnetic radiation from the processing element can be reflectedelectromagnetic radiation, transmitted electromagnetic radiation, and/ordispersed electromagnetic radiation. Whether the detector analyzesreflected, transmitted, or dispersed electromagnetic radiation may bedictated by the structural parameters of the optical computing device aswell as other considerations known to those skilled in the art. Inaddition, emission and/or scattering of the fluid or a phase thereof,for example via fluorescence, luminescence, Raman, Mie, and/or Raleighscattering, can also be monitored by the optical computing devices.

As used herein, the term “optically interact” or variations thereofrefers to the reflection, transmission, scattering, diffraction, orabsorption of electromagnetic radiation either on, through, or from oneor more processing elements (i.e., integrated computational elements) ora substance. Accordingly, optically interacted light refers toelectromagnetic radiation that has been reflected, transmitted,scattered, diffracted, or absorbed by, emitted, or re-radiated, forexample, using an integrated computational element, but may also applyto interaction with a substance, such as a fluid.

As used herein, the term “fluid” refers to any substance that is capableof flowing, including particulate solids, liquids, gases, slurries,emulsions, powders, muds, glasses, mixtures, combinations thereof, andthe like. The fluid may be a single phase or a multiphase fluid. In someembodiments, the fluid can be an aqueous fluid, including water, brines,or the like. In other embodiments, the fluid may be a non-aqueous fluid,including organic compounds, more specifically, hydrocarbons, oil, arefined component of oil, petrochemical products, and the like. In someembodiments, the fluid can be acids, surfactants, biocides, bleaches,corrosion inhibitors, foamers and foaming agents, breakers, scavengers,stabilizers, clarifiers, detergents, a treatment fluid, fracturingfluid, a formation fluid, or any oilfield fluid, chemical, or substanceas found in the oil and gas industry and generally known to thoseskilled in the art. The fluid may also have one or more solids or solidparticulate substances entrained therein. For instance, fluids caninclude various flowable mixtures of solids, liquids and/or gases.Illustrative gases that can be considered fluids according to thepresent embodiments, include, for example, air, nitrogen, carbondioxide, argon, helium, methane, ethane, butane, and other hydrocarbongases, hydrogen sulfide, combinations thereof, and/or the like.

As used herein, the term “substance,” or variations thereof, refers toat least a portion of matter or material of interest to be tested orotherwise evaluated using the optical computing devices describedherein. The substance includes the characteristic of interest, asdefined above, and may be any fluid, as defined herein, or otherwise anysolid substance or material such as, but not limited to, rockformations, concrete, solid wellbore surfaces, and solid surfaces of anywellbore tool or projectile (e.g., balls, darts, plugs, etc.).

According to the disclosed embodiments, employing discriminant analysistechniques and processing with optical computing devices using one ormore ICE components can further aid in reducing the time required toaccurately determine the characteristic (e.g., the chemical and/orphysical properties) of a sample substance being analyzed. Thisdetermination may be performed in parallel with the collection ofoptical measurements in situ. While ICE technology generally enables anear real-time, in situ measurement of a sample substance, qualitativeuses of discriminant analysis techniques using ICE technology can infer,for example, a particular chemical grouping based on opticalspectroscopic data. For example, by using qualitative discriminantanalysis, an unknown sample substance may be narrowed and otherwisereadily assigned to a particular chemical grouping of known samplesubstances. As a result, operators may then be enabled to optimizesubsequent measurement parameters and/or procedures (e.g., handling andsafety precautions) before traditional sampling of the substance isundertaken. Moreover, qualitative discriminant analysis may allow anoperator to decide that a particular calibration is more suitable inpredicting a specific analytical concentration as opposed to otherpotential calibration models (e.g., in deciding the difference betweenlight oil and heavy oil).

In addition to qualifying a sample into a particular group, discriminateanalysis can further aid in the quantitative analysis of a chemicalproperty of an unknown sample substance. By using quantitativediscriminant analysis techniques, a more narrow grouping of calibrationsmay be employed, thereby increasing the accuracy and efficiency ofoptical computing device measurements. For example, in the explorationand extraction of hydrocarbons, many different types of oil can beexpected to be encountered. To avoid having to undertake multiplelab-based calibrations in which an infinite number of oil samples willbe measured against an infinite number of prepared calibrations, a smalllibrary of calibrations can be compiled and quantitative discriminantanalysis techniques may be applied to such a library to point to, forexample, a small number or series of calibrations. As a result, anunknown oil sample may be classified and/or otherwise quantified usingICE technology without the need to employ a large library ofcalibrations which can be very time-consuming and expensive to develop.

The use of discriminant analysis in conjunction with optical computingdevices may provide several advantages. In some applications, forexample, using discriminant analysis techniques in conjunction withoptical computing devices using ICE components can facilitate increasedflexibility in supporting tools in field use by enabling subtle changesto be made in the calibration of the tool without requiring a sample tobe extracted and analyzed in the lab.

As mentioned above, the processing element used in the exemplary opticalcomputing devices discussed herein may be an integrated computationalelement (ICE), referred to herein as an “ICE component”. In operation,an ICE component is capable of distinguishing electromagnetic radiationrelated to a characteristic of interest of a substance (e.g., a fluid oran object present in the fluid) from electromagnetic radiation relatedto other components of the substance. Referring to FIG. 1, illustratedis an exemplary ICE 100 that may include a plurality of alternatinglayers 102 and 104, such as silicon (Si) and SiO₂ (quartz),respectively. In general, these layers 102, 104 consist of materialswhose index of refraction is high and low, respectively. Other examplesof materials might include niobia and niobium, germanium and Germania,MgF₂, SiO, and other high and low index materials known in the art. Thelayers 102, 104 may be strategically deposited on an optical substrate106. In some embodiments, the optical substrate 106 is BK-7 opticalglass. In other embodiments, the optical substrate 106 may be anothertype of optical substrate, such as quartz, sapphire, silicon, germanium,zinc selenide, zinc sulfide, or various plastics such as polycarbonate,polymethylmethacrylate (PMMA), polyvinylchloride (PVC), diamond,ceramics, combinations thereof, and the like.

At the opposite end (e.g., opposite the optical substrate 106 in FIG.1), the ICE 100 may include a layer 108 that is generally exposed to theenvironment of the device or installation. The number of layers 102, 104and the thickness of each layer 102, 104 are determined from thespectral attributes acquired from a spectroscopic analysis of acharacteristic of the substance being analyzed using a conventionalspectroscopic instrument. It should be understood that the exemplary ICE100 in FIG. 1 does not in fact represent any particular characteristicof a given substance, but is provided for purposes of illustration only.Consequently, the number of layers 102, 104 and their relativethicknesses, as shown in FIG. 1, bear no correlation to any particularcharacteristic. Moreover, those skilled in the art will readilyrecognize that the materials that make up each layer 102, 104 (i.e., Siand SiO₂) may vary, depending on the application, cost of materials,and/or applicability of the material to the given substance beinganalyzed.

In some embodiments, the material of each layer 102, 104 can be doped ortwo or more materials can be combined in a manner to achieve the desiredoptical characteristic. In addition to solids, the exemplary ICE 100 mayalso contain liquids and/or gases, optionally in combination withsolids, in order to produce a desired optical characteristic. In thecase of gases and liquids, the ICE 100 can contain a correspondingvessel (not shown), which houses the gases or liquids. Exemplaryvariations of the ICE 100 may also include holographic optical elements,gratings, piezoelectric, light pipe, and/or acousto-optic elements, forexample, that can create transmission, reflection, and/or absorptiveproperties of interest.

The multiple layers 102, 104 exhibit different refractive indices. Byproperly selecting the materials of the layers 102, 104 and theirrelative thickness and spacing, the ICE 100 may be configured toselectively pass/reflect/refract predetermined fractions ofelectromagnetic radiation at different wavelengths. Each wavelength isgiven a predetermined weighting or loading factor. The thickness andspacing of the layers 102, 104 may be determined using a variety ofapproximation methods from the spectrum of the characteristic or analyteof interest. These methods may include inverse Fourier transform (IFT)of the optical transmission spectrum and structuring the ICE 100 as thephysical representation of the IFT. The approximations convert the IFTinto a structure based on known materials with constant refractiveindices.

The weightings that the layers 102, 104 of the ICE 100 apply at eachwavelength are set to the regression weightings described with respectto a known equation, or data, or spectral signature. Whenelectromagnetic radiation interacts with a substance, unique physicaland chemical information about the substance may be encoded in theelectromagnetic radiation that is reflected from, transmitted through,or radiated from the substance. This information is often referred to asthe spectral “fingerprint” of the substance. The ICE 100 may beconfigured to perform the dot product of the electromagnetic radiationreceived by the ICE 100 and the wavelength dependent transmissionfunction of the ICE 100. The wavelength dependent transmission functionof the ICE is dependent on the layer material refractive index, thenumber of layers 102, 104 and the layer thicknesses. The ICE 100transmission function is then analogous to a desired regression vectorderived from the solution to a linear multivariate problem targeting aspecific component of the sample being analyzed. As a result, the outputlight intensity of the ICE 100 is related to the characteristic oranalyte of interest.

The optical computing devices employing such an ICE may be capable ofextracting the information of the spectral fingerprint of multiplecharacteristics or analytes within a substance and converting thatinformation into a detectable output regarding the overall properties ofthe substance. That is, through suitable configurations of the opticalcomputing devices, electromagnetic radiation associated withcharacteristics or analytes of interest in a substance can be separatedfrom electromagnetic radiation associated with all other components ofthe substance in order to estimate the properties of the substance inreal-time or near real-time.

According to one or more embodiments disclosed herein, discriminantanalysis calculations, processing, methods, and/or techniques may beapplied to output signals from optical elements, such as ICE components,or optical computing devices that employ such optical elements, in orderto classify or quantify two or more sets of sample substances. As knownin the art, discriminant analysis generally involves the determinationof a linear equation configured to predict which group a particular case(e.g., a sample substance) belongs to. The form of a generaldiscriminant analysis equation or function is shown in the followingequation:

D=v ₁ X ₁ +v ₂ X ₂ +v ₃ X ₃ . . . =v _(i) X _(i) +a   Equation (1)

where D is the discriminant function; v is the discriminant coefficientor weight for that variable; X is the respondent's score for thatvariable; a is a constant; and i is the number of predictor variables.The v's are un-standardized discriminant coefficients that serve tomaximize the distance between the means of the criterion (dependent)variable. After using an existing set of data to calculate thediscriminant function and classify known sample substances, any newunknown sample substance can then be classified, qualified, or otherwisequantified.

One or more exemplary methods or processes that use discriminantanalysis in conjunction with a plurality of ICE components will now bedescribed. In particular, FIGS. 2-7 may depict or otherwise illustrate amethod for using qualitative discriminant analysis in conjunction with aplurality of ICE components in order to classify or otherwise categorizeunknown sample substances. Those skilled in the art will readilyappreciate that the ICE components and the discriminant analysistechniques or methods described herein may be used with any type orconfiguration of optical computing devices as known by those skilled inthe art.

Referring first to FIG. 2, illustrated is an exemplary transmittancespectrum 200 corresponding to a plurality of ICE components that haveoptically interacted with a particular substance. The substance may be,for example, a formation fluid, and each ICE component may be configuredto detect a different characteristic of the formation fluid spanned overan optical wavelength of interest. FIG. 2 shows the convolutedtransmittance spectrum 200 in simulation for four out of ten ICEcomponents that were used in the following examples to opticallyinteract with or otherwise monitor the substance. For purposes ofclarity, the simulated transmittance spectrum 200 for the remaining sixICE components were omitted, but it should be noted that the dataprovided in the described embodiment is representative of data derivedfrom a total of ten ICE components.

In operation, each ICE component acts as a multi-band filter and itsrespective optical response is linearly or non-linearly correlated witha particular characteristic (i.e., a particular physical or chemicalproperty) of the substance (i.e., the formation fluid). In theillustrated example, for instance, ICE #1 may be configured to detectsaturates in the substance, ICE #2 may be configured to detect aromaticsin the substance, ICE #3 may be configured to detect resins in thesubstance, and ICE #4 may be configured to detect gas-to-oil ratio (GOR)in the substance. The remaining six ICE components not depicted in FIG.2 for clarity purposes may be configured to detect other characteristicsof the substance, such as asphaltenes, methane, ethane, propane, butaneand propane, and density, for example.

Referring to FIG. 3, with continued reference to FIG. 2, illustrated areoptical responses 300 of the plurality of ICE components used to createthe transmittance spectrum 200 of FIG. 2. In particular, FIG. 3illustrates the optical responses 300 for each of the ten ICE componentsin view of five different known fluid groups selected from an opticaldatabase. As used herein, the term “optical database” refers to adatabase that contains or otherwise has stored therein a full-rangecollection of fluid spectra over a variety of fluid types with eachsample spectrum being measured with a commercial or traditionalspectrometer under a number of specified or predetermined temperatureand pressure combinations. As illustrated, the five fluid groups includewater, light oil, dark oil, live oil condensate, and gas. Since each ICEcomponent is configured to detect a different characteristic of the fiveor more fluid groups (i.e., saturates, aromatics, resins, asphaltenes,methane, ethane, propane, butane and propane, density, and GOR), theoptical responses 300 for each ICE component are indicative of aconcentration of each characteristic present in each of the fluidgroups.

In one or more embodiments, an operator may be able to reference theoptical responses 300 of FIG. 3 and generally identify the type orcategory of the sample fluid. In other words, once the optical responses300 are recorded, a qualitative-type determination can be manually madethrough mere curve matching against known fluid types. As will beappreciated by those skilled in the art, the optical responses 300 ofeach ICE component may be measured in actual scale or normalized scale,in transmittance domain or in absorbance domain, without departing fromthe scope of the disclosure.

According to embodiments of the present disclosure, however, the opticalresponses 300 of FIG. 3 may be used to help train a neural network toperform qualitative discriminant analysis on an unknown sample substanceor fluid, thereby helping to classify or categorize the unknownsubstance into a particular grouping or category. In exemplary usage,the trained neural network may help an operator classify an unknownformation fluid as heavy, medium, or light, for example. In otherapplications, the trained neural network may help classify an unknownformation fluid as having high or low concentrations of saturates,aromatics, resins, and asphaltenes (SARA). Such qualitative discriminantgrouping or categorization may prove advantageous in enabling operatorsto optimize parameters or procedures.

Referring now to FIG. 4, with continued reference to FIGS. 2 and 3,illustrated is an example neural network structure 400 that may betrained and subsequently used to classify or otherwise categorize anunknown sample substance. As used herein, the term “neural network”refers to a multivariate classification and/or regression (e.g.,qualitative and/or quantitative) model for discriminant analysis. Insome embodiments, as illustrated, the neural network structure 400 mayinclude a plurality of ICE components as inputs. In particular, theneural network structure 400 may be configured to receive or otherwiseprocess the optical responses 300 of FIG. 3 from the ten ICE componentsdescribed therein. As depicted, the neural network 400 may receive anoptical response input from ICE #1 configured to relate saturatesindicator to fluid type, an optical response input from ICE #2configured to relate aromatics indicator to fluid type, an opticalresponse input from ICE #3 configured to relate resins indicator tofluid type, and an optical response input from ICE #4 configured torelate gas-to-oil ratio (GOR) indicator to fluid type.

The optical responses from the remaining six ICE components of theoriginal ten, are represented by the ellipses 402 and are not fullyillustrated in the neural network structure 400 for the sake of clarity.As briefly mentioned above, these remaining six ICE components areconfigured to relate the indicator of such characteristics asasphaltenes, methane, ethane, propane, butane and propane, and densityto the fluid type in a sample fluid substance.

The neural network structure 400 may further have two hidden layers andfive outputs that are configured to classify a sample substance as atleast one of water, condensed fluid, light oil, dark oil (i.e., mediumand heavy oils) and gas (CH₄ and CO₂). The neural network structure 400may be generated and otherwise supported using a computer system thathas a computer software program stored on a non-transitorycomputer-readable medium. In some embodiments, the computer softwareprogram may be MATLAB Neural Network Toolbox, but may alternatively beany other computer software capable of creating a neural network andapplying principles of discriminant analysis thereto. For example, thecomputer software program may also include the IBM SPSS Statisticscomputer program, without departing from the scope of the disclosure.

Each output of the neural network 400 may represent or otherwise providea probability value ranged from 0 to 1 of a particular fluid type forthe given sample substance. Such probability values may be coded in fiveoutputs. In some embodiments, for example, an output of pure water maybe coded as [1 0 0 0 0], an output of live oil condensate may be codedas [0 1 0 0 0], an output of dead light oil may be coded as [0 0 1 0 0],an output of dead dark oil may be coded as [0 0 0 1 0], and an output ofpure gas may be coded as [0 0 0 0 1].

In the illustrated example, 208 fluid samples of a known chemical andphysical make-up were selected to help train the neural network 400. Inparticular, the 208 fluid samples consisted of 24 water samples, 21 liveoil condensate samples, 70 light oil (dead) samples, 70 dark oil (dead)samples, and 23 gas samples measured at different (but known)temperature and pressure combinations. The ten simulated ICE componentswere then optically-interacted with the 208 selected fluid samples, andthe resulting optical responses from the ten simulated ICE componentswere used to train the neural network structure 400. The resultingcoefficient matrices are represented in the neural network structure 400by W₁, b₁ on the first hidden layer, W₂, b₂ on the second hidden layer,and W₃, b₃ on the output layer.

Referring to FIGS. 5 a-5 e, with continued reference to FIG. 4,illustrated are exemplary classification outputs derived while trainingthe neural network structure 400 of FIG. 4. In particular, the variousclassification outputs of FIGS. 5 a-5 e compare the neural network 400prediction with a random noise corrupted target value on the fiveoutputs, respectively, over all calibration and validation samples. Forexample, FIG. 5 a displays the water index (i.e., the first output inthe neural network 400) for each of the fluid samples. As illustrated,the water index registers a value of “1” for the first 24 samples and avalue of “0” for the remaining samples, thereby indicating that thefirst 24 samples are water and the remaining samples are non-watersamples.

Similarly, FIG. 5 b displays the live oil condensate index (i.e., thesecond output in the neural network 400) for each of the fluid samples.According to FIG. 5 b, it can be concluded that samples 25 to 45 arelive oil condensate fluid samples and the other samples are not. FIG. 5c displays the dead light oil index (i.e., the third output in theneural network 400) for each of the samples, and it can be concludedthat samples 46 to 115 are dead light oil while the other samples arenot. FIG. 5 d displays the dead dark oil index (i.e., the fourth outputin the neural network 400) for each of the samples, and it can beconcluded that samples 116 to 185 are classified as dead dark oil whilethe others are not. FIG. 5 e displays the gas index (i.e., the fifthoutput in the neural network 400) for each of the samples, and it can beconcluded that the last 23 samples are gas samples while the others arenot.

Now that the classification model of the neural network 400 has beentrained using known pure samples corresponding to the particular outputindices depicted in FIGS. 5 a-5 e, the neural network 400 may be used orotherwise employed to estimate corresponding proportions of similarsubstances present in unknown fluid samples or mixtures. In other words,unknown fluid samples may be processed with, by, or otherwise using theneural network 400 such that a qualitative discriminant analysis of eachfluid sample may be obtained or undertaken in order to determineproportions of the fluid samples which correspond to the five outputs ofthe neural network 400 (i.e., pure water, live oil condensate, deadlight oil, dead dark oil, and pure gas).

FIGS. 6 and 7 demonstrate such an application of using the trainedneural network 400 by testing three unknown samples, shown as Sample #1,Sample #2, and Sample #3. Specifically, FIG. 6 illustrates the opticalor spectral responses 600 of the ten ICE components upon opticallyinteracting with the three unknown fluid samples. The optical responses600 of the ten ICE components may then be inputted into or otherwiseapplied to the classification model or trained neural network 400. FIG.7 illustrates the fluid type index outputs for each of the three unknownfluid samples as corresponding to its respective optical response 600after having been processed using the trained neural network 400.Accordingly, FIG. 7 depicts a predicted substance or fluid type for eachof the samples as derived through the classification model.

As indicated in FIG. 7, by applying the classification model of thetrained neural network 400, Sample #1 is classified as dead dark oilsince the 4th index registers “1” and the other indices register “0”.Sample #2, on the other hand, is highlighted as likely fluid of live oilcondensate since the 2nd index registers “1” and the other indicesregister “0” or near “0”. A non-zero output is registered on the 4thindex for Sample #2, thereby indicating that Sample #2 likely containsat least some dark oil. Since the dark oil index is smaller than “0.1”,however, its slight influence may be generally ignored by an operatorfor purposes of qualitative analysis. In other words, the predictedsubstance type of Sample #2 corresponds to the highest probability ascalculated by the classification model, which is more likely tocorrespond to live oil condensate over dark oil.

The testing results for Sample #3 provide an output of about “0.3” forlive oil condensate and about “0.7” for light oil. Such results mayindicate to an operator that the optical response for Sample #3possesses features or characteristics of both basic fluids. Since Sample#3 registers more predominantly as a light oil as opposed to a live oilcondensate, an operator may be able to qualitatively classify Sample #3as a light oil.

As described in greater detail below, however, the intermediate indexvalues for Sample #3 may be used as weighting factors for quantitativecalibration or discrimination analysis if each type of fluid (i.e., liveoil condensate and light oil) has its own calibration model. Indetermining a particular chemical concentration or quantity of theSample #3, for example, the solution could be the weighted sum of theoutputs of the live oil condensate model and the condensed fluid model.In other words, the predicted substance type for Sample #3 maycorrespond to a mathematical linear combination between classificationmodels for each of live oil condensate and light oil. Such adetermination is at least one example of quantitative discriminantanalysis.

The neural network 400 of FIG. 4 is depicted and described merely forillustrative purposes and therefore should not be considered as limitingto the scope of the present disclosure. Rather, the present disclosurefurther contemplates the generation and training of neural networks thatuse more or less than 10 ICE components and provide results in more orless than five output indices, without departing from the scope of thedisclosure.

In addition to qualifying or categorizing an unknown sample substanceinto a particular chemical grouping based on optical spectroscopic data,as generally described above, discriminant analysis can also aid in thequantitative determination of a chemical property or characteristic ofan unknown sample. According to one or more embodiments, opticalresponses from a plurality of ICE components based on known samples fromthe optical database may be used as inputs to build one or morequantitative calibration models for quantitative discriminating analysiswith non-linear neural networks. More particularly, and with referenceto FIG. 8, illustrated is another example neural network structure 800similar in some respects to the neural network structure 400 of FIG. 4.

Similar to the neural network 400, the neural network 800 may begenerated and otherwise processed using a computer system that employs acomputer software program (e.g., MATLAB Neural Network Toolbox, IBM SPSSStatistics, etc.) stored on a non-transitory computer-readable medium.Moreover, similar to the neural network 400, the neural network may betrained using a plurality of optical responses for a correspondingplurality of ICE components in view of several different fluid samplesselected from the optical database. In the present embodiment, theoptical responses used to train the neural network 800 may be similar tothose shown in FIG. 3 above, but with more variations in data rangesince it may encompass more fluid samples.

The neural network structure 800 may also use a plurality of ICEcomponents and their respective optical responses as inputs. Inparticular, the neural network structure 800 may use a response from ICE#1 configured to detect saturates, a response from ICE #2 configured todetect aromatics, ICE #3 configured to detect resins, and ICE #4configured to detect gas-to-oil ratio (GOR). Responses from anyremaining ICE components are represented by the ellipses 802 and are notfully illustrated in the neural network structure 800 for clarity.

Unlike the neural network 400 of FIG. 4 which classifies a samplesubstance using five outputs, the neural network 800 may be configuredto quantify a sample substance in terms of fluid concentration or otherproperties or characteristics of interest over six outputs. As depictedin FIG. 8, for example, the exemplary neural network structure 800 maybe configured for the quantitative analysis of fluid concentrations ofmethane, saturates, aromatics, resins, asphaltenes, and API gravity asthe six model outputs.

The neural network 800 is depicted and described merely for illustrativepurposes and should not be considered as limiting to the scope of thepresent disclosure. Rather, the present disclosure further contemplatesthe generation and training of a neural network that provides aquantitative model that results in more or less than six output indices(including a single output). Moreover, the fluid properties to bepredicted through quantitative calibration are also not limited to theones indicated in FIG. 8. Instead, other fluid properties, includingconcentrations of C₂-C₆, CO₂, H₂O, H₂S, and GOR, for example, may alsobe predicted with either a single output or multi-output neural networkquantitative models using the same or different ICE components and theirrespective optical responses as inputs.

Although the application of the neural networks 400, 800 of FIGS. 4 and8, respectively, may be different in purpose (i.e., pattern recognitionand/or classification for qualitative analysis using the neural network400, and function approximation for quantitative analysis using theneural network 800), the model structures in each case may be somewhatsimilar, such as being implemented with two hidden-layer neuralnetworks. The transfer function used on each hidden layer may be anon-linear, hyperbolic tangent sigmoid function. In contrast, thetransfer function used on the output layer may be a linear function.

Computing the net outputs of each neural network 400, 800 may follow thefollowing equations:

$\begin{matrix}{a_{1} = {{f_{1}\left( n_{1} \right)} = \frac{^{n_{1}} - ^{- n_{1}}}{^{n_{1}} + ^{- n_{1}}}}} & {{Equation}\mspace{14mu} (2)} \\{n_{1} = {{W_{1}*P} + b_{1}}} & {{Equation}\mspace{14mu} (3)} \\{a_{2} = {{f_{2}\left( n_{2} \right)} = \frac{^{n_{2}} - ^{- n_{2}}}{^{n_{2}} + ^{- n_{2}}}}} & {{Equation}\mspace{14mu} (4)} \\{n_{2} = {{W_{2}*a_{1}} + b_{2}}} & {{Equation}\mspace{14mu} (5)} \\{a_{3} = {{f_{3}\left( n_{3} \right)} = {n_{3} = {{W_{3}*a_{2}} + b_{3}}}}} & {{Equation}\mspace{14mu} (6)}\end{matrix}$

where P is a forward input vector, W₁, b₁, W₂, b₂, and W₃, b₃ are theconnecting or weighting matrices or vectors and n₁, n₂, n₃, a₁, a₂, anda₃ are net inputs and net outputs at different layers. In exemplaryoperation, each neural network 400, 800 feeds the forward input vector Pthough multiple layers to calculate the respective output(s).

Referring now to FIGS. 9 a-9 f, with continued reference to FIG. 8,illustrated are six comparison plots for six quantitative calibrationmodels, respectively, according to one or more embodiments. Inparticular, FIGS. 9 a-9 f compare the prediction of the quantitativeneural network 800 with actual measurements for the six separatecalibration models for over more than forty different sample fluids.FIG. 9 a illustrates a comparison plot 902 a for methane concentrations;FIG. 9 b illustrates a comparison plot 902 b for saturatesconcentrations; FIG. 9 c illustrates a comparison plot 902 c foraromatics concentrations; FIG. 9 d illustrates a comparison plot 902 dfor resins concentrations; FIG. 9 e illustrates a comparison plot 902 efor asphaltenes concentrations; and FIG. 9 f illustrates a comparisonplot 902 f for API gravity concentrations. For each of these plots 902a-f, a linear fit equation and correlation coefficient R are generatedto show the proximity of neural network (NN) prediction Y and the actualtarget value T. Typically, a value of near “1” for slope and near “0”for intercept in the linear fit equation will indicate high accuracy ofcalibration model if the correlation coefficient value R is also closeto 1.

The relative calibration error, which may be determined using theroot-mean-squared error over the calibration data points divided by theparameter range calculated from the boundary values of x-axis in eachplot, is from the minimum 1.77% (corresponding to methane) to themaximum 3.67% (corresponding to asphaltenes) in these examples. At leastone advantage of using the neural network 800 for quantitativediscriminating analysis is its robustness in including samples of allfluid types into a single model. Moreover, sample selection may not berequired or crucial in general, which may prove advantageous inconvenience for quantitative calibration model development.

In other embodiments, however, partial least square (PLS) regression maybe used to develop linear quantitative calibration models using themulti-ICE component optical responses as inputs. In such embodiments,sample selection and optical response transformation might be requiredto construct a fluid type based model for better application.

It should be noted that for both the non-linear neural network and thelinear PLS quantitative analysis, the particular fluid property orcharacteristic is not only modeled with the optical response of itscorresponding ICE component as an input alone, but also modeled withinputs of other optical responses from other ICE components to overcomelimitations associated with single ICE component realization. Forexample, saturates are not modeled only with the optical response of ICE#1 (i.e., the ICE component configured to detect saturates) as a loneinput optical response, but saturates may also be modeled with inputs ofother optical responses from the remaining ICE components, therebyproviding a multi-band filter application.

Also, it will be appreciated that multiple designs for ICE componentsconfigured to detect the same property or characteristic may be used ascalibration inputs for quantitative model development. For example,saturates may be detected or otherwise monitored using several differentdesigns of ICE components configured to detect saturates.

Referring now to FIGS. 10 and 11, illustrated are cross plots 1000 and1100, respectively, providing quantitative measurement data derived fromthe trained neural network 800 upon testing three unknown samples, shownas Sample #1, Sample #2, and Sample #3. In particular, background datain the cross plot 1000 of FIG. 10 depicts SARA concentration (i.e., thesum of saturates, aromatics, resins and asphaltenes) versus methaneconcentration over a variety of known fluid samples derived from theoptical database. Similarly, the cross plot 1100 of FIG. 11 depicts APIgravity versus the sum of asphaltenes and resins concentration overfluid samples derived from the optical database. The three samples maybe the same three unknown samples described above with reference toFIGS. 6 and 7. Accordingly, the cross plots 1000 and 1100 may show howqualitative analysis can be combined with quantitative analysis todiscriminate/identify fluid properties of one or more unknown samples.

With reference to FIG. 10, the known sample points of the database thatland on or are otherwise generally located near the X-axis are samplesthat contain little to no SARA components but instead exhibit highmethane concentrations. Such samples indicate typical gascharacteristics. On the other hand, the sample points that land on orare otherwise generally located on or near the Y-axis are samples thatcontain little or no methane but instead exhibit differingconcentrations of SARA. Such samples can be indicative of dead oils andother dead fluids, such as toluene, hexane, naphthalene, and siliconeoil. The origin point (0,0) in the cross plot 1000 represents substanceslike pure water, CO₂, N₂, ethane, and propane without CH₄ and SARA inits composition. As can be appreciated, the known sample points of thedatabase not located on the X-axis or the Y-axis have both SARA andmethane in composition.

The resulting qualitative analysis described above in FIG. 7 indicatesthat Sample #1 is likely dark oil, Sample #2 is likely live oilcondensate, and Sample #3 is a combination of live oil condensate(approximately 30%) and light oil (approximately 70%). By applying thequantitative calibration models of the neural network 800, theconcentration of the three testing samples on methane, saturates,aromatics, resins, asphaltenes, and GOR may be calculated or otherwisedetermined. The corresponding concentrations of SARA and methane foreach sample may be plotted in the cross plot 1000 of FIG. 10. Accordingto the cross plot 1000, for example, the methane and SARA concentrationfor Sample #1 is about 0.0003 and about 0.8309 (g/mL), respectively, forSample #2 is about 0.0906 and about 0.6047 (g/mL), respectively, and forSample #3 is about 0.044 and about 0.7484 (g/mL). Such determinationsagree with the previous findings of FIG. 7 for each sample.

With reference to FIG. 11, the API gravity can be converted from the oilstock tank condition density, which may be a good indicator of oil types(e.g., dark oil and light oil) when used in conjunction with asphaltenesand resins. The sample points that exhibit high API gravity and lowconcentration of asphaltenes and resins content are typically indicativeof light oils. On the other hand, the sample points that exhibit low APIgravity and high concentration of asphaltenes and resins are typicallyindicative of dark oils. As depicted in FIG. 11, the co-relation betweenAPI gravity and the concentration of asphaltenes and resins is notpurely linear. Rather, significant variations over particular dataranges can often be observed, depending on many other factors.

After applying the API gravity quantitative calibration model of theneural network 800, and recalculating the concentration of asphaltenesplus resins, the cross plot 1100 of FIG. 11 may be able to show thecorresponding points for each of Samples #1, #2, and #3. As indicated inthe cross plot 1100, Sample #1 appears to fit the characterization ofdark oil because of its relatively high concentration of asphaltenesplus resins and low concentration of API gravity. The stock tank oildensity can be high for live oil condensate (i.e., the gas contents canbe removed), leading to relatively low API gravity for sample #2, andits asphaltenes plus resins concentration is reasonably lower than darkoil. The partial light oil characteristics of Sample #3 make its APIgravity higher than the other samples. Moreover, its concentration ofasphaltenes plus resins is within the normal range, as shown in thecross plot 1100.

In some embodiments, a qualitative analysis of an unknown sample mayfirst be undertaken or performed using a trained multivariateclassification model (such as the neural network 400 of FIG. 4) when newdata is acquired to initially determine the category or type of fluid.Subsequently, a quantitative analysis of the unknown sample using aquantitative model (such as the neural network 800 of FIG. 8) may beundertaken or performed in order to calculate or otherwise quantify oneor more fluid properties in detail and compare them with informationstored in an optical database to evaluate if the quantitative predictionis reasonable. A general agreement between qualitative analysis andquantitative analysis may prove advantageous in helping an operator oranalyst make a more confident determination or decision. Anydisagreement between the qualitative and quantitative analyses, however,may indicate the limitation of existing neural network models anddatabase and help flag the uncertainty of prediction.

Several applications may be optimized using the calibration modelsdescribed herein. For example, the trained neural network 800 may proveadvantageous in performing discriminant analyses to optimize thequantitative calibration of an optical computing device for a particularcharacteristic or property of an unknown substance under study. In someembodiments, quantitative calibration models may be trained or otherwisegenerated for a large number of fluid types, thereby generating a largelibrary of calibrations. Theoretically, quantitative calibration modelscould be generated for every type of oil worldwide, for example. Uponencountering an unknown downhole fluid, such as an oil, the largelibrary of quantitative calibration models may prove advantageous indirecting an operator to the exact oil composition and concentration.Such a process of generating calibration models for every type of oil,however, could be fairly time-consuming and otherwise inefficient.

In other embodiments, however, a small library of quantitativecalibration models could be generated for a few types of fluids, such astypes of oils. Upon encountering an unknown downhole fluid, the smalllibrary of quantitative calibration models may prove advantageous indirecting an operator to the nearest neighbor of the true unknown fluid.While such an embodiment only requires the development of a small numberof calibrations, as opposed to the large library described in theprevious embodiment, the small number of calibrations may only providean operator with an approximation.

In yet other embodiments, the small library of quantitative calibrationmodels described above may fail to provide an adequate approximation or“nearest neighbor” to the unknown substance or fluid. In suchembodiments, a new calibration model may be generated based on theclosest calibrations from the small library. The closest calibrationmodels may be configured or otherwise used to fine-tune a more accuratecalibration for quantifying the concentration of the unknown substanceor fluid.

In yet other embodiments, the calibration models described herein mayprove advantageous in use with other sensing or measurement devices,such as spectrometers, densitometers, temperature and pressure gauges,etc. For example, the calibration models may prove useful inrecalibrating such devices and/or instruments, such that the instrumentsare able to perform more precisely.

It should be noted that while the embodiments discussed herein useintegrated computational elements as an optical element, it is furthercontemplated herein to use any other optical element known to thoseskilled in the art. For example, suitable optical elements that may beused in any of the disclosed embodiments include, but are not limitedto, holographic optical elements, acousto-optic tunable filters, andliquid crystal tunable filters.

The methods described herein, or large portions thereof, may beautomated at some point such that a computerized system may beprogrammed to create a neural network and apply discriminant analysistechniques thereto in order to qualify or quantify an unknown samplesubstance. Computer hardware used to implement the various methods andalgorithms described herein can include a processor configured toexecute one or more sequences of instructions, programming stances, orcode stored on a non-transitory, computer-readable medium. The processorcan be, for example, a general purpose microprocessor, amicrocontroller, a digital signal processor, an application specificintegrated circuit, a field programmable gate array, a programmablelogic device, a controller, a state machine, a gated logic, discretehardware components, an artificial neural network, or any like suitableentity that can perform calculations or other manipulations of data. Insome embodiments, computer hardware can further include elements suchas, for example, a memory (e.g., random access memory (RAM), flashmemory, read only memory (ROM), programmable read only memory (PROM),electrically erasable programmable read only memory (EEPROM)),registers, hard disks, removable disks, CD-ROMS, DVDs, or any other likesuitable storage device or medium.

Executable sequences described herein can be implemented with one ormore sequences of code contained in a memory. In some embodiments, suchcode can be read into the memory from another machine-readable medium.Execution of the sequences of instructions contained in the memory cancause a processor to perform the process steps described herein. One ormore processors in a multi-processing arrangement can also be employedto execute instruction sequences in the memory. In addition, hard-wiredcircuitry can be used in place of or in combination with softwareinstructions to implement various embodiments described herein. Thus,the present embodiments are not limited to any specific combination ofhardware and/or software.

As used herein, a machine-readable medium will refer to any medium thatdirectly or indirectly provides instructions to a processor forexecution. A machine-readable medium can take on many forms including,for example, non-volatile media, volatile media, and transmission media.Non-volatile media can include, for example, optical and magnetic disks.Volatile media can include, for example, dynamic memory. Transmissionmedia can include, for example, coaxial cables, wire, fiber optics, andwires that form a bus. Common forms of machine-readable media caninclude, for example, floppy disks, flexible disks, hard disks, magnetictapes, other like magnetic media, CD-ROMs, DVDs, other like opticalmedia, punch cards, paper tapes and like physical media with patternedholes, RAM, ROM, PROM, EPROM and flash EPROM.

Therefore, the present invention is well adapted to attain the ends andadvantages mentioned as well as those that are inherent therein. Theparticular embodiments disclosed above are illustrative only, as thepresent invention may be modified and practiced in different butequivalent manners apparent to those skilled in the art having thebenefit of the teachings herein. Furthermore, no limitations areintended to the details of construction or design herein shown, otherthan as described in the claims below. It is therefore evident that theparticular illustrative embodiments disclosed above may be altered,combined, or modified and all such variations are considered within thescope of the present invention. The invention illustratively disclosedherein suitably may be practiced in the absence of any element that isnot specifically disclosed herein and/or any optional element disclosedherein. While compositions and methods are described in terms of“comprising,” “containing,” or “including” various components or steps,the compositions and methods can also “consist essentially of” or“consist of” the various components and steps. All numbers and rangesdisclosed above may vary by some amount. Whenever a numerical range witha lower limit and an upper limit is disclosed, any number and anyincluded range falling within the range is specifically disclosed. Inparticular, every range of values (of the form, “from about a to aboutb,” or, equivalently, “from approximately a to b,” or, equivalently,“from approximately a-b”) disclosed herein is to be understood to setforth every number and range encompassed within the broader range ofvalues. Also, the terms in the claims have their plain, ordinary meaningunless otherwise explicitly and clearly defined by the patentee.Moreover, the indefinite articles “a” or “an,” as used in the claims,are defined herein to mean one or more than one of the element that itintroduces. If there is any conflict in the usages of a word or term inthis specification and one or more patent or other documents that may beincorporated herein by reference, the definitions that are consistentwith this specification should be adopted.

1. A method, comprising: optically interacting a plurality of opticalelements with one or more known substances, each optical element beingconfigured to detect a particular characteristic of the one or moreknown substances; generating an optical response from each opticalelement corresponding to each known substance, wherein each knownsubstance corresponds to a known spectrum stored in an optical database;and training a neural network to provide a discriminant analysisclassification model for an unknown substance, the neural network usingeach optical response as inputs and one or more fluid types as outputs,and the outputs corresponding to the one or more known substances. 2.The method of claim 1, wherein at least one of the plurality of opticalelements is an integrated computational element.
 3. The method of claim1, further comprising: optically interacting the plurality of opticalelements with an unknown substance, thereby generating an unknownsubstance optical response; applying the unknown substance opticalresponse to the classification model; and outputting a predictedsubstance type corresponding to the unknown substance.
 4. The method ofclaim 3, wherein the predicted substance type corresponds to a highestprobability as calculated by the classification model.
 5. The method ofclaim 3, wherein the predicted substance type corresponds to amathematical linear combination of at least two substance types of theone or more known substances, the mathematical linear combinationproviding a new fluid type.
 6. The method of claim 5, furthercomprising: adding the new fluid type to the one or more knownsubstances such that the new fluid type becomes one of the one or moreknown substances; generating a new optical response from each opticalelement corresponding to each known substance; and training a new neuralnetwork using each new optical response as input and thereby providing anew classification model.
 7. The method of claim 3, further comprising:generating at least one quantitative model corresponding to at least oneof the one or more known substances; using the predicted substance typecorresponding to the unknown substance to select the at least onequantitative model; applying the selected at least one quantitativemodel to provide an unknown substance property prediction; andvalidating the unknown substance property prediction by referencing theoptical database.
 8. The method of claim 1, wherein opticallyinteracting the plurality of optical elements with the one or more knownsubstances comprises generating a plurality of classification outputsthat compare a prediction from the classification model with a randomnoise corrupted target value corresponding to each of the one or moreoutputs.
 9. The method of claim 1, further comprising quantifying withthe one or more outputs a concentration of the unknown substance withreference to the one or more known substances.
 10. A method, comprising:training a neural network having one or more outputs corresponding toone or more known substances, thereby generating a multivariateclassification model for discriminant analysis of an unknown substance;introducing into the multivariate classification model an unknownsubstance optical response corresponding to the unknown substance; andoutputting a predicted substance type corresponding to the unknownsubstance from the one or more outputs.
 11. The method of claim 10,wherein training the neural network comprises: optically interacting aplurality of optical elements with the one or more known substances,each optical element being configured to detect a particularcharacteristic of the one or more known substances; generating anoptical response from each optical element corresponding to each knownsubstance, wherein each known substance corresponds to a known spectrumstored in an optical database; and applying each optical response to theneural network.
 12. The method of claim 11, wherein at least one of theplurality of optical elements is an integrated computational element.13. The method of claim 11, wherein introducing into the multivariateclassification model the unknown substance optical response comprises:optically interacting the plurality of optical elements with the unknownsubstance, thereby generating the unknown substance optical response;and applying the unknown substance optical response to the multivariateclassification model.
 14. The method of claim 10, wherein the predictedsubstance type corresponds to a highest probability as calculated by themultivariate classification model.
 15. The method of claim 10, whereinthe predicted substance type corresponds to a mathematical linearcombination of at least two substance types of the one or more knownsubstances, the mathematical linear combination providing a new fluidtype.
 16. The method of claim 15, further comprising: adding the newfluid type to the one or more known substances such that the new fluidtype becomes one of the one or more known substances; generating a newoptical response from each optical element corresponding to each knownsubstance; and inputting each new optical response into the multivariateclassification model, thereby providing a new multivariateclassification model.
 17. The method of claim 10, further comprisingclassifying the predicted substance type with respect to at least one ofthe one or more known substances.
 18. The method of claim 10, furthercomprising quantifying with the one or more outputs a concentration ofthe unknown substance with reference to the one or more knownsubstances.